{"type":"ScholarlyArticle","title":"UNOP: Physics-Constrained Unsupervised Neural Operator for Long-Horizon PDE Learning on Generalized Geometries","authors":[{"name":"Xinrui Cheng","slug":"xinrui-cheng","given":"Xinrui","family":"Cheng","affiliation":""},{"name":"Tianqi Zhao","slug":"tianqi-zhao","given":"Tianqi","family":"Zhao","affiliation":""},{"name":"Zhaodong Zhang","slug":"zhaodong-zhang","given":"Zhaodong","family":"Zhang","affiliation":""},{"name":"Ngai Wong","slug":"ngai-wong","given":"Ngai","family":"Wong","affiliation":""},{"name":"Zhongjie Wang","slug":"zhongjie-wang","given":"Zhongjie","family":"Wang","affiliation":""},{"name":"Ruihan Hu","slug":"ruihan-hu","given":"Ruihan","family":"Hu","affiliation":""}],"abstract":"Unsupervised learning of neural operators is constrained by numerical instability, causing predictions to diverge in long-horizon rollouts. To address this, we present a physics-constrained unsupervised neural operator for long-horizon PDE learning on generalized geometries (UNOP). This framework replaces differential constraints with integral consistency for stable, label-free learning. Unlike prior works, UNOP is built upon Latent Integral Physics Embedding (LIPE), which enforces physical consistency through integral constraints. To extend integral formulations to generalized geometries, the Geometry-Agnostic Latent Adapter (GALA) projects them onto a unified latent grid of PDE inputs, providing a regularized domain for spatial integral evaluation. Based on this shared embedding, the Gated Spectral Evolution Operator (GSEO) performs stable temporal integration while retaining spatial regions with sharp gradients and fine-scale structures, with the evolution constrained by the LIPE objective. Experiments on 1D, 2D, and 3D benchmarks show UNOP outperforms state of the art methods, reducing error accumulation by up to 60% in \r\n20-step rollouts. Code is available at https://github.com/chengxinrui/UNOP.","doi":"10.24963/ijcai.2026/469","url":"https://ijcai.org/proceedings/2026/469","pdf":"https://ijcai.org/proceedings/2026/0469.pdf","markdown":"https://ijcai.org/proceedings/2026/469.md","bibtex":"https://ijcai.org/proceedings/2026/bibtex/469","volume":{"slug":"2026","title":"Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2026","url":"https://ijcai.org/proceedings/2026/","year":2026,"location":"Bremen, Germany","dates":"15-21 August 2026","editors":"Diego Calvanese","isbn":"978-1-956792-09-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2026"},"section":"Machine Learning","track":"Main Track","number":469,"pages":{"first":4215,"last":4223},"keywords":["Machine Learning: Unsupervised learning","Machine Learning: Deep learning architectures","Multidisciplinary Topics and Applications: Physical sciences"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}